A particle in Electric and Magnetic field

[Abdul.119]

Homework Statement

A charge q is released in crossed E and B fields: E is oriented along y axis; B is oriented about z axis
Derive the equation of motion of q

Homework Equations

The Attempt at a Solution

I'm not sure what equation I should use here, the only equation that I have which gives Force in terms of E and B is: F = q(E+v×B) , so I was thinking of using that, and set it equal to Newton's law F = m r'' , where r'' = {x'',y'',z''} , am I correct like that?

 

[Suraj M]

What exactly is r"?

 

[Abdul.119]

What exactly is r"?

r is just position, and by r'' I mean it is r derived twice so that it is acceleration

 

[Suraj M]

Okay firstly if the object is moving without deflection even in the presence of a magnetic and electric field, what would be the resultant force on the body?

 

[Abdul.119]

Okay firstly if the object is moving without deflection even in the presence of a magnetic and electric field, what would be the resultant force on the body?

In general it should be F = ma

 

[Suraj M]

What would be the shape of the path of the object?

 

[ehild]

Homework Statement

A charge q is released in crossed E and B fields: E is oriented along y axis; B is oriented about z axis
Derive the equation of motion of q

Homework Equations

The Attempt at a Solution

I'm not sure what equation I should use here, the only equation that I have which gives Force in terms of E and B is: F = q(E+v×B) , so I was thinking of using that, and set it equal to Newton's law F = m r'' , where r'' = {x'',y'',z''} , am I correct like that?

Yes, it is correct.
You know the direction of the electric and magnetic field vectors. Write them out in vector form, and determine the components F_x, F_y, F_z of the force. Note that the force depends on the velocity, that is, (x'_x, y'_y, z'_z) , Then you get three equations in the form mx"=F_x, my"=F_y, mz"=F_z.